Problem: Express this product in scientific notation: $(4.60\times 10^{2})\times (5.00\times 10^{3})$
Answer: Start by collecting like terms together. $= (4.60\times 5.00) \times (10^{2}\times 10^{3})$ When multiplying exponents with the same base, add the powers together. $= 23.0 \times 10^{2\,+\,3}$ $= 23.0 \times 10^{5}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $23.0$ is the same as $2.300 \times 10$ $ = {2.300 \times 10} \times 10^{5} $ $= 2.300\times 10^{6}$